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1. Statistics Assignment | Sample Homework | www.expertsmind.com
Probability
3DP, a Luxembourg-based company plans to develop and sell highly specialized 3D printers.
The cost of product development is estimated at EUR 50,000.-, irrespective of whether or
not the product is finally marketed. The company owners put the odds of a successful
product launch at 70%.
The market for such a sophisticated piece of equipment is rather limited: the number of
orders is assumed to follow a binominal distribution. In the first quarter will definitely not
exceed 20, and the probability of placing a single order is evaluated at 30%. The variable cost
would amount to EUR 3,300.- and the final price tag would be set at EUR 15,500.-
As the company owners have secured the patent for their innovative technology, a viable
alternative to launching the production is simply to sell the license. USAin3D, a U.S.-based
company is a potential buyer offering USD 7,800.- (non-negotiable) and 3DP owners must
take the final decision before three months.
By that time, of course, the EUR/USD exchange rate will surely change. A friend of 3DP
owners, who happens to be a financial analyst, estimates that in three months’ time the
EUR/USD exchange rate will fall by not more than -10.504% with the probability of 2.5%. To
make this estimate, he assumed that the percentage change of the EUR/USD exchange rate
follows a normal distribution with (three-month) volatility of 5.9535%. The current (spot)
EUR/USD exchange rate is equal 1.3684 (dollars per one euro).
Questions:
1. Estimate the Expected Monetary Value (EMV) of the two options: product launch and
selling the license. What should be the decision by the 3DP owners based solely on financial
considerations? Is it a strong decision from the business point of view?
2. How would the EUR/USD exchange rate need to change in order for the 3DP owners to
change their mind? What is the probability associated with such a fx movement?
Calculate the answers and present them in a short PowerPoint presentation

2. Regression
The following table presents the monthly data on the sales volume (col 2) and promotional
spending (col 3) of a company. Column (4) shows an index of economic activity in the local
economy.
Answer the following questions:
· What is the correlation between:
◦ sales volume and the promotional spending?
◦ sales volume and the economic activity index?
◦ promotional spending and the economic activity index?
Given the sizes of correlation, do you think there is a valid case for running a
regression? Logically, which variable would you consider as dependent?

3. · Using excel (either reglinp or Analysis ToolPak), run the regression of sales
volume (dependent variable) on a constant (intercept) and promotional
spending. Write down explicitly the regression equation, setting out the
estimated coefficients as well as the associated standard errors.
◦ What is the interpretation of the coefficients?
◦ How about their signs? Do they make intuitive sense?
◦ Are they statistically significant?
◦ (Optional) What is the forecast sales volume assuming that the
promotional spending amounts to EUR 150,000? What is the 95%
confidence interval around this point forecast (hint: use formulas on
p. 396 of the textbook).
· Run another regression, this time adding index of economic activity as the
second explanatory variable. What are the results now? Write down explicitly
the regression equation, setting out the estimated coefficients as well as the
associated standard errors.
◦ Has the quality of fit improved substantially?
◦ Purely from statistical (not business) perspective, is there a strong
case for adding the index of economic activity as one of the
explanatory variables? Why?
Q.2 Solution
a) Correlation coefficient between sales volume and promotional spending is 0.9244
b) Correlation coefficient between sales volume and economic activity index is –
0.2918
c) Correlation coefficient between promotional spending and economic activity
index is
- 0.1698

4. Q.3 solution
The regression equation is
y = 6581.382 + 318.0483*x
where y = sales volume x= the promotional spending
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.924442
R Square 0.854593
Adjusted R Square 0.847984
Standard Error 3986.267
Observations 24
ANOVA
df SS MS F Significance F
Regression 1 2.05E+09 2.05E+09 129.299911 1.10996E-10
Residual 22 3.5E+08 15890321
Total 23 2.4E+09
Standard
Coefficients Error t Stat P-value Lower 95% Upper 95%
Intercept 6581.3816 1222.619174 5.383018 2.094E-05 4045.824658 9116.938591
Promotion 318.04833 27.97009901 11.37101 1.11E-10 260.0418935 376.054763
a) Interpretation of regression coefficient:
Expected change in the value of Y (sales) for the unit change in the value of
independent variable x.
b) Since coefficient is positive it means that X and Y change in the same direction. If X
increases,
then Y increases.
c) Since P-value corresponding to coefficients intercept and promotion is less than 0.05
it means that the coefficients are statistically significant.

5. Q.4 solution
The regression equation is
y = 19636.49204 + 309.9691647*x1 - 1.044373301*x2
where
y=sales volume
x1= the promotional spending
x2= Economy activity index
Regression Statistics
Multiple R 0.93443355
R Square 0.873166059
Adjusted R Square 0.861086636
Standard Error 3810.603587
Observations 24
ANOVA
df SS MS F Significance F
Regression 2 2.1E+09 1.05E+09 72.28541 3.83683E-10
Residual 21 3.05E+08 14520700
Total 23 2.4E+09
Upper
Coefficients SE t Stat P-value Lower 95% 95%
Intercept 19636.49204 7535.964 2.605704 0.016508 3964.597221 35308.39
Promotion 309.9691647 27.13158 11.42467 1.79E-10 253.545965 366.3924
-
Economy activity index -1.044373301 0.595562 -1.75359 0.094086 2.282913066 0.194166
a) Since the value of adjusted R-square has increased as compared to the previous
model from 84 % to 86 %so we can say that quality of fit has improved.
b) Even if the value of adjusted R-square has increased but the p-value corresponding
to the regression coefficient of the index of economic activity is greater than 0.05
which means that it is not statistically significant.